Arch form first developed as a musical technique. In music, arch form is a sectional structure based on repetition, in reverse order, of all or most musical sections such that the overall form is symmetric, most often around a central movement. The sections need not be repeated verbatim but must at least share thematic material.
These variations on a theme create interest through interplay among “memory, variation, and progression”. Though the form appears to be static and to deny progress, the pairs of movements create an “unidirectional process” with the center, and the form “actually engenders specific expressive possibilities that would otherwise be unavailable for the work as a whole”.
As a technique for writing, the writer creates a sentence that takes a broad theme and condenses it to give her story a particular meaning within the major theme. Theme is the big concept, and often too broad: love, honor, justice, betrayal, loyalty, family, courage, duty. A Thematic Statement refines the broad idea into a shape and metaphor which applies directly to the current tale, imbuing the story with the power of the theme within a seed.
As the story moves forward, repeats of that statement are used with variations, which are often tunings, but can also be subtly altered to present other points of view and even counter views which would normally muddle the focus, but instead reinforce the center.